A model of hematopoietic bone marrow apoptosis during growth factor deprivation in combination with a cytokine

Theor Biol Med Model. 2018 Jun 21;15(1):8. doi: 10.1186/s12976-018-0080-2.


Background: The process by which blood cells are formed is referred to as hematopoiesis. This process involves a complex sequence of phases that blood cells must complete. During hematopoiesis, a small fraction of cells undergo cell death. Causes of cell death are dependent upon various factors; one such factor being growth factor deprivation.

Methods: In this paper, a mathematical model of hematopoiesis during growth factor deprivation is presented. The model consists of a set of three coupled differential delay equations. Phase plane and linear stability analysis are performed in order to locate and determine stability of fixed points. Numerical simulations of the governing equations are run and provide a visual display of the behavior of the stem cell population undergoing growth factor deprivation. In addition, the effect of cytokine administration is incorporated in the model in an effort to understand how cytokine administration can offset the negative effects of apoptosis caused by growth factor deprivation.

Conclusions: The model produces qualitatively similar results to that observed during serum deprivation. The model captures apoptosis levels of cells at different time points. Additionally, it is shown that cytokine administration stabilizes the stem cell count.

Keywords: Differential delay equations; Growth factor deprivation; Hematopoiesis.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Apoptosis / physiology*
  • Bone Marrow / metabolism*
  • Bone Marrow / pathology
  • Cytokines / deficiency*
  • Hematopoiesis / physiology*
  • Hematopoietic Stem Cells / metabolism
  • Hematopoietic Stem Cells / pathology
  • Humans
  • Intercellular Signaling Peptides and Proteins / deficiency*
  • Models, Theoretical*


  • Cytokines
  • Intercellular Signaling Peptides and Proteins